Decentralized diffusion-based learning under non-parametric limited prior knowledge

We study the problem of diffusion-based network learning of a nonlinear phenomenon, $m$, from local agents’ measurements collected in a noisy environment. For a decentralized network and information spreading merely between directly neighboring nodes, we propose a non-parametric learning algorithm, that avoids raw data exchange and requires only mild $\mathit{\text{a}}\mathit{\text{priori}}$ knowledge about $m$. Non-asymptotic estimation error bounds are derived for the proposed method. Its potential applications are illustrated through simulation experiments.